This chapter discusses a survey of nonlinear regression models, with an emphasis on the theory of estimation and hypothesis testing rather than on computation and applications. The advent of advanced computer technology has made it possible for the econometrician to estimate an increasing number of nonlinear regression models. Nonlinearity arises in diverse ways in econometric applications. Perhaps the simplest and best-known case of nonlinearity in econometrics arises as the observed variables in linear-regression models. Another well-known case is the distributed-lag model in which the coefficients on the lagged exogenous variables are specified to decrease with lags in certain nonlinear fashion, such as geometrically declining coefficients. In both of these cases, nonlinearity appears only in parameters but not in variables. More general nonlinear models are used in the estimation of production functions and demand functions. Even a simple CobbDouglas production function cannot be transformed into linearity if the error term is added rather than multiplied.
